IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 28, NO. 3, APRIL 2018 4006504
Influence of Compaction During Reaction Heat
Treatment on the Interstrand Contact Resistances of
Nb
3
Sn Rutherford Cables for Accelerator Magnets
Edward Collings Collings, Mike D. Sumption
, Milan Majoros, Xiaorong Wang
, Daniel R. Dietderich,
Konstantin Yagotyntsev, and Arend Nijhuis
Abstract—The high field superconducting magnets required for
ongoing and planned upgrades to the Large Hadron Collider (LHC) will be wound with Nb3Sn Rutherford cables for which reason studies of Nb3Sn strand, cable, and magnet properties will continue to be needed. Of particular importance is field quality. The amplitudes of multipoles in the bore fields of dipole and quadrupole magnets, induced by ramp-rate-dependent coupling currents, are under the control of the interstrand contact resistances—crossing-strand,Rc, adjacent strand,Ra, or a combination of them,Reff.
Although two decades ago it was agreed that for the LHC Rc should be in the range 10–30µΩ, more recent measurements of LHC quadrupoles have revealedRc values ranging from 95 to 230µΩ. This paper discusses ways in which these values can be achieved. In a heavily compacted cableReffcan be tuned to some
predictable value by varying the width of an included stainless steel (effectively “insulating”) core. But cables are no longer heav-ily compacted with the result that the crossing strands of the im-pregnated cable are separated by a thick epoxy layer that behaves like an insulating core. If a stainless steel core is actually present, Reffmust be independent of core width. Since there is no guarantee
that a fixed predetermined amount of interlayer separation could be reproduced from winding to winding it would be advisable to include a full width core.
Index Terms—Nb3Sn accelerator magnets, Nb3Sn Rutherford cables, Nb3Sn strands, interstrand contact resistance.
I. INTRODUCTION
R
UTHERFORD cables wound with Nb3Sn strands will be used in all the high field superconducting magnets re-quired for ongoing and planned upgrades to the large hadron collider (LHC): the high luminosity LHC (High Lumi LHC, HL-LHC, 11 and 12 T), a higher energy LHC (HE-LHC, 16 T), Manuscript received August 24, 2017; accepted December 4, 2017. Date of publication January 23, 2018; date of current version March 8, 2018. This work was supported by the U.S. Department of Energy, Office of High Energy Physics, under Grant DE-SC0011721 (OSU) and Grant DE-AC02-05CH11231 (LBNL). (Corresponding author: Mike D. Sumption.)E. Collings, M. D. Sumption, and M. Majoros are with the Department of Materials Science and Engineering, Center for Superconducting and Mag-netic Materials, Ohio State University, Columbus, OH 43210 USA (e-mail: sumption.3@osu.edu).
X. Wang and D. R. Dietderich are with the Superconducting Magnet Group, Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720 USA.
K. Yagotyntsev and A. Nijhuis are with the Energy, Materials, and Systems Group, the University of Twente, Enschede 7522, The Netherlands.
Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TASC.2018.2796595
TABLE I STRANDDETAILS
Cable type HQ QXF
Strand source, type OST-RRP, 108/127 OST-RRP, 108/127 Strand diam,ds, mm 0.778 0.852
SC filament count 108 108
Filament OD,d0,μm 51.5 62.2 Eff. fil. OD,deff,μm 61.8 72.4
and a very high energy future circular collider (FCC, 16 T) [1]. The HL-LHC upgrade project [2] will involve four pairs of Nb3Sn-wound quadrupoles with peak coil fields of 12 T [2] along with several 11 T 11 m long Nb3Sn dipoles [3]. A sug-gested HE-LHC will consist of a ring of about 1280 14 m long 16 T Nb3Sn dipoles housed in the existing LHC tunnel [4]. The proposed FCC is estimated to require 4578 15 m long 16 T Nb3Sn dipoles [5] housed in a new 1000 km circumference tunnel. Accordingly a 16 T Nb3Sn dipole will be developed to satisfy the requirements of both the FCC and the HE-LHC. In contributing to that development, the US Magnet Development Program will be exploring the limits of applicability of Nb3Sn for high field magnets [6]. Studies of Nb3Sn cable and strand properties will continue to be needed. Reported elsewhere are the effects of core type, placement, and width and heat treatment condition on interstrand coupling properties of Nb3Sn cables [7]–[9]. Magnetization due to ramp-rate-dependent interstrand coupling currents in cables induces multipoles in the bore fields of dipole and quadrupole magnets [10], [11]. As a contribution to this topic, and indirectly to the US LHC Accelerator Research Program (LARP), we report on the influence of reaction heat treatment conditions on the interstrand contact resistances of Nb3Sn Rutherford cables.
II. EXPERIMENTAL
A. Preparation of Cables for Measurement
Several meters of stainless steel cored HQ- and QXF-type Nb3Sn Rutherford cables, wound at the Lawrence Berkeley Na-tional Laboratory (LBNL), were provided to Ohio State Uni-versity’s Center for Superconducting and Magnetic Materials (OSU-CSMM). Strand and cable details are given in Tables I and II, and reference [8]. In preparation for measurement 1051-8223 © 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
4006504 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 28, NO. 3, APRIL 2018 TABLE II CABLEDETAILS LBNL name ∗ HQ1020ZB HQ1021ZB QXF 1055z-C QXF 1055z-K QXF 1055z-Q QXF 1055z-O QXF 1055z-M QXF 1055z-D OSU name H1 H2 Q1 Q2 Q3 Q4 Q5 Q6 Strand count 35 35 35 40 40 40 40 40 40 Pack factor∗∗, % 85.54 85.55 85.53 87.04 86.89 87.03 86.98 86.80 87.38 Core width, mm 0 8 – 11.9 15.9 15.4 14.3 13.3 0 Core cover, W,% 0 60 – 72 96 93 86 80 0
∗Mixture of 1020 and 1021with cores extracted,∗∗This is the initial packing factor at the time of cable manufacture.
cable samples were cut to length (50 cm) insulated, reaction heat treated (RHT) and epoxy impregnated. Two different pro-cedures were applied: (1) Two stacks of HQ cable were uniax-ially compressed to 20 MPa at CSMM in a bolt-down fixture before being sent to LBNL for RHT. After return to CSMM the stacks were wrapped in teflon film, placed in an aluminum mold, uniaxially compressed to 5 MPa, and vacuum impregnated with CTD-101 resin. (2) Six stacks of QXF cable pieces was returned to LBNL for mounting under zero applied pressure and RHT; a similar bolt-down fixture was used but this time adjusted so as to confine the cable stack within a space just large enough to let it freely expand 1.5% in width and 4.5% in thickness. The final impregnation also took place under zero applied pressure.
Fig. 1 illustrates the pronounced effect of uniaxial pressure on the compaction of the cable stack during reaction and epoxy impregnation. As a result of compaction the upper and lower cable layers are tightly squeezed together; in the absence of compaction they can become widely separated. This can mod-ify the strand packing density from the as manufactured cable packing factor of Table II.
B. Measurement of Interstrand Contact Resistance
The interstrand contact resistances (ICR) were derived from the results of AC loss measurement using equipment located in the Energy, Materials, and Systems Laboratory of the Univer-sity of Twente. The cable stacks to be measured were exposed to transverse AC fields of amplitude Bm = 400 mT and
fre-quencies, f, of up to 60 mHz applied perpendicular to the broad faces of the cables (the “face-on, FO, orientation). Total loss,Qt, could be measured both by He-boil-off calorimetry [8] and pick-up coil magnetometry. The calorimeter was calibrated against ohmic loss of a 25Ω resistor; the magnetometer was calibrated against the calorimetric loss of cable stack H2 near its maxi-mumQt(f). The results of the magnetic loss measurements are
presented in Fig. 2.
III. DATAANALYSIS
A. Reff Versus Core-Coverage, W, From the MagneticQt(f)
orQcoup(f) Data
The total energy dissipated per cycle of a cable exposed to a face-on (FO) alternating field isQt = Qh + QcoupwhereQhis
the strand-based persistent current (“hysteretic”) loss andQcoup, is the interstrand coupling loss. As explained in [8] the coupling loss per cycle per m3 of cable (width, w, thickness, t, strand
Fig. 1. (a) Compacted cored cable H2 (b) uncompacted cored cable Q5.
count, N, transposition pitch, 2Lp) exposed to an FO field lin-early ramping at a rate dB/dt is given by:
Qcoup (FO)= 4 3 w t LpBm N2 20 1 Rc + 20 N3Ra dB dt (1) whereRcandRaare the cable’s crossover and adjacent ICRs.
Then after transforming dB/dt to a sinusoidal frequency, f, according to (dB/dt)= (π2/2)fB m, as explained in [12] we find: Qcoup (FO)(f) = π2 30 w t LpBm2N2 1 Rc + 20 N3Ra .f (2)
COLLINGS et al.: INFLUENCE OF COMPACTION DURING REACTION HEAT TREATMENT 4006504
Fig. 2. Total face-on magnetization loss,Qt = Qh+ Qcoup, as function of frequency, f, for the H series and QXF series cables. The persistent current components,Qh, are the f= 0 intercepts.
= π2 30 w t LpB2mN2 1 Reff .f (3)
which indicates thatReff the “effective interstrand contact re-sistance” defined by[1/Rc+ 20/(N3Ra)]−1can obtained from the initial slope ofQtversus f. As a final step experimental plots ofReff versus core-coverage, W, can be constructed.
B. CUDI-Calculated Plots ofReff Versus Core-Coverage, W
An expression for coupling power,Pcoup= Qcoup.f , starts with Eqn (1), substitutesf = (dB/dt)(2/π2Bm) [12], and takes
the form Pcoup= 4 30π2 w t LpN2 1 Reff dB dt 2 (4) The fortran program CUDI [13] enables Pcoup to be cal-culated as function of W for a set of Rutherford cables with insulating cores of various widths and positions within the ca-ble. Then as explained elsewhere [7], [8] Eqn (4) enables the conversion of the CUDI-calculatedPcoupto anReff which leads to calculated plots ofReff versus W.
IV. RESULTS
A. Reff Versus W for Compacted HQ-Type Cables
Since 2008 this group has conducted about 17 AC-loss-based ICR measurements of uncored and cored Nb3Sn Rutherford ca-bles that had been compacted to 20 MPa uniaxial pressure before and during RHT [7]. As a result of crossover interstrand sinter-ing the uncored cables exhibited an average Rc of 0.26 μΩ.
Then as W increased from 32% to 90% (full width) Reff in-creased monotonically up to 246μΩ [7], Fig. 3. As expected
the data for H1 and H2 are members of this group. Fig. 3 also shows the CUDI-modelledReff. Selected as inputs to the model areRc= 0.26 μΩ and Ra= 0.2 μΩ (following [14] wherein
it was recommended thatRashould be small but not less than
Fig. 3. Reff versus core cover for a previously studied assortment of com-pacted Nb3Sn cables (o), the present compacted cables H1 and H2 () (see Table III), and a CUDI simulation based on defined Rc= 0.26 μΩ and Ra= 0.2 μΩ (—).
TABLE III
MAGNETICALLY MEASUREDReff AND THE DEDUCEDRaVALUES
Cable Type HQ QXF Stack name H1 H2 Q1 Q2 Q3 Q4 Q5 Q6 W, % 0 60 71 95 94 86 80 0 Rr m e f f,μΩ 0.39 1.66 31.1 60.3 72.8 83.4 57.1 68.7 Ra, nΩ∗ 9.7 18.8 22.1 26.1 17.8 21.5 ∗R
a based on (20/N3)Re f ffor the QXF cables.
0.2μΩ) and the core is assumed to be centered. Many of the
experimental points lie below the model curve indicating that for those cables the cores were biased to one edge [7].
B. Reff Versus W for Uncompacted QXF-Type Cables
Listed in Table III are the magnetically measuredReff values based onQt(f) and Eqn (3)). The low deduced Ra values, in
the range of 18–26 nΩ, indicate unexpectedly tight adjacent strand contact ([8], Fig. 4). In setting up the CUDI model we recognize the wide separation between the upper and lower cable layers, Fig. 1(b), by assigning a very large value to Rc, viz. 100,000 μΩ. Under this condition Reff turns out to be independent of W. Curves of Reff versus W for Ra= 26 nΩ and 18 nΩ are presented in Fig. 4. Inserted in the figure are the experimental points for cables Q2–Q6 (Q1 is neglected as an outlier).
V. DISCUSSION
The true index of field error is the coupling magnetization,
Mcoup, which based on Eqn. (1) is given in general by Mcoup= 1 60 w t LpN2 1 Rc + 20 N3Ra .dB dt (5)
Large values of Rc clearly favour small Mcoup but in the interests of current sharing and stability some compromises have been sought. Some two decades ago it was agreed that
4006504 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 28, NO. 3, APRIL 2018
Fig. 4. ExperimentalReff versus core cover data for QXF cables Q2–Q6 (o). The lines are CUDI simulations based onRc = 0.1 Ω with Ra= 26 nΩ (—)
and 18 nΩ (—); they represent W-independent Reffvalues of 86μΩ and 60 μΩ,
respectively.
for the LHC Rc should be in the range 15 ± 5 μΩ [15] or 20± 10 μΩ [16]. The prefactor N3allows
Raitself to be small although it was recommended to be no smaller than 0.2 μΩ
[14]. As pointed out recently [8] with reference to [7] and [17] numerous measurements of LHC dipoles and quadrupoles have revealedRc values very much larger than the 20μΩ “target”.
Measurements of dipoles yielded Rcs well above 50 μΩ and
measurements of quadrupoles using various techniques yielded
Rcs ranging from 95μΩ to 230 μΩ for an approximate average
value (based on [7]) of 160μΩ.
When translating these results into other cables it must be recognized that Mcoup is proportional not just to 1/Reff but also to the other cable design parameters (w/t),Lp, and N2. So
to preserve the sameMcoupwhen replacing an LHC-inner cable with design parameters 7.94, 55 mm, and 282with an uncored
QXF-type cable, Eqn (6), with parameters 10.1, 54.5 mm, and 402would requireR
eff (orRc) to be increased by a factor 2.6. Mcoup,uncore= 1 60 w t LpN2 1 Rc .dB dt (6) Mcoup,core= 1 60 w t LpN2 20 N3Ra .dB dt (7)
For the uncored cable Eqn (6) showsMcoup,uncoreto be pro-portional to 1/Rc. The introduction of a fully insulating core reduces the proportionality to 20/(N3Ra), Eqn (7). So not only
isMcoup,corereduced by a huge factor, further decreases would accompany increases in N.
Measurements of LHC quadrupoles have revealedRcvalues around 160μΩ which at an LHC ramp-rate of 7.5 mT/s leads,
via Eqn (6), to anMcouparound 0.8 kA/m. To raiseRcfrom its “compacted value” of 0.26μΩ would require the insertion of
an insulating core in which caseMcoup would depend onRa. Comparing Eqns (6) and (7) to keepMcoupfixed the value ofRa needed would be 160× 20/N3 = 50 nΩ a value consistent with the results presented here. The compacted cable needs a full core to removeRcfrom the equation. Since in the uncompacted case
the crossing strands are separated by a thick epoxy layer,Reff is essentially “infinite” whether the core is present or not; i.e.,
Reff is independent of core width as illustrated in Fig. 4. Since there is no guarantee that such a condition could be reproduced from winding to winding it would be advisable to include a full width core.
ACKNOWLEDGMENT
The cables were wound by H.C. Higley (LBNL), heat treated at LBNL (QXF cables) and Brookhaven National Laboratory (HQ cables, A.K, Ghosh). J. Yue and R. Avonce (Hyper Tech Research) performed the vacuum impregnation.
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